Gerhard, N., Caviedes-Voullième, D., Müller, S. et al. (1 more author) (2015) Multiwavelet-based grid adaptation with discontinuous Galerkin schemes for shallow water equations. Journal of Computational Physics, 301. 265 - 288. ISSN 0021-9991
Abstract
We provide an adaptive strategy for solving shallow water equations with dynamic grid adaptation including a sparse representation of the bottom topography. A challenge in computing approximate solutions to the shallow water equations including wetting and drying is to achieve the positivity of the water height and the well-balancing of the approximate solution. A key property of our adaptive strategy is that it guarantees that these properties are preserved during the refinement and coarsening steps in the adaptation process.The underlying idea of our adaptive strategy is to perform a multiresolution analysis using multiwavelets on a hierarchy of nested grids. This provides difference information between successive refinement levels that may become negligibly small in regions where the solution is locally smooth. Applying hard thresholding the data are highly compressed and local grid adaptation is triggered by the remaining significant coefficients. Furthermore we use the multiresolution analysis of the underlying data as an additional indicator of whether the limiter has to be applied on a cell or not. By this the number of cells where the limiter is applied is reduced without spoiling the accuracy of the solution.By means of well-known 1D and 2D benchmark problems, we verify that multiwavelet-based grid adaptation can significantly reduce the computational cost by sparsening the computational grids, while retaining accuracy and keeping well-balancing and positivity.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Elsevier Inc. This is an author produced version of a paper subsequently published in Journal of Computational Physics. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Grid adaptivity; Multiresolution analysis; Multiwavelets; Discontinuous Galerkin; Shallow water flows; Positivity-preserving; Well-balancing; Limiters; Shock detection |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Civil and Structural Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 30 Oct 2015 13:24 |
Last Modified: | 03 Sep 2017 20:31 |
Published Version: | http://dx.doi.org/10.1016/j.jcp.2015.08.030 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.jcp.2015.08.030 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:90531 |